Knee biomechanics variability before and after total knee arthroplasty: an equality of variance prospective study

This study evaluated gait variability in patients before and after total knee arthroplasty (TKA) using the equality of variance method to determine where variability differences occur in the movement cycle. Twenty-eight patients underwent TKA with cruciate-sacrificed implants. Patients underwent motion analysis which measured knee biomechanics as they walked overground at their preferred pace before and 12 months after TKA. Equality of variance results were compared with 14 healthy controls of similar age. Before surgery, patients had reduced knee extension moment variability throughout the early stance phase (4–21% gait cycle, p < 0.05) compared to controls. Knee power variability was lower preoperatively compared to controls for most of the stance phase (0–13% and 17–60% gait cycle, p < 0.05). Sagittal knee moment and power variability further decreased following TKA. Knee extension moment variability was lower postoperatively throughout stance phase compared to preoperatively (4–22% and 36–60% gait cycle, p < 0.05) and compared to controls (4–30% and 45–60% gait cycle, p < 0.05). Knee power variability remained lower following TKA throughout stance phase compared to preoperatively (10–24% and 36–58% gait cycle, p < 0.05) and controls (3–60% gait cycle, p < 0.05). TKA patients may be less stable, and this may be in part due to an unresolved adaptation developed while awaiting TKA surgery and the cruciate sacrificing design of the implants utilized in this study.

Pain and impaired mobility are a daily reality for those living with symptomatic knee osteoarthritis (OA) 1 .As knee OA progresses, greater pain and stiffness occur at the knee joint, which ultimately requires surgical intervention with a total knee arthroplasty (TKA).Despite TKA being a successful surgery, 20% of patients remain dissatisfied after their TKA and often report loss of stability, decreased functional outcomes, reduced knee range of motion, greater difficulty performing daily activities compared to their age-matched peers 2 , and their gait becomes less variable 3 .The question remains as to why patients are still unsatisfied, which could be related to knee instability after TKA.
Orthopaedic surgeons evaluate knee joint instability by assessing knee joint laxity; however, self-reported instability is unrelated to knee joint laxity 4 .Greater knee joint instability can cause a loss of balance and lead to an eventual fall 5 .The measure of knee joint laxity assesses static stability but falls generally occur during movements, implying deficits in dynamic stability 6,7 .Researchers have assessed the dynamic stability of the knee by evaluating the variability of temporospatial and knee biomechanical measures during gait 6,8 .
Gait variability is the amplitude of the fluctuations in the time series with respect to the mean of kinematic (e.g., joint angles) or kinetic (e.g., joint moments) measurements 9 .Several methods to estimate the amount of gait variability are routinely used and include standard deviation 10 , Lyapunov exponent 6 , or the coefficient of variation (CV) 11,12 .Methods such as standard deviation and coefficient of variation provide a measure of global variability, which integrates the variability across the time domain to yield a single scalar value.A review on gait variability in patients with knee OA highlighted that variability remains lower than healthy controls before and after a TKA 3 .However, this was determined using single scalar values of gait variability, so it is unknown where in the gait cycle these variability differences occur.Understanding where significant differences in variance occur in a movement cycle may identify certain motor impairments.This could help influence rehabilitation interventions in individuals with knee OA before or after undergoing a TKA.

Equality of variance analysis
Knee biomechanics variability between the pre-TKA, post-TKA, and CTRL groups is presented in Fig. 1.Within Fig. 1, the line graph illustrates the group mean knee biomechanics and standard deviation, whereas the horizontal bars represent where in the gait cycle variability was significantly (p < 0.05) different between the two groups.In general, patients had less variability post-TKA compared to pre-TKA.Sagittal knee angle variability was lower post-TKA compared to pre-TKA throughout terminal stance (37-49% gait cycle (%)); sagittal knee extension moment variability was lower post-TKA during mid-stance (4-22%) and terminal stance (36-60%); and knee power variability was also lower during mid-stance (10-24%) and terminal stance (36-58%).
Knee biomechanics variability differences between pre-TKA and CTRLs were less consistent.Sagittal knee angle variability was greater in the pre-TKA group throughout most of the single-limb support (14-53%) and at mid-swing (72-89%).Sagittal knee moment variability was greater in the CTRL in the early stance phase (4-21%), but greater in the pre-TKA throughout the terminal stance (39-59%).Knee power variability was greater in the CTRL group throughout loading response (0-13%) and from mid-stance to just before toe-off (17-60%).www.nature.com/scientificreports/Sagittal knee angle variability was greater in the post-TKA group compared to the CTRL group during mid-swing (73-91%).However, the CTRL group had greater sagittal knee moment and knee power variability compared to the post-TKA group.Sagittal knee moment variability was greater throughout mid-stance (4-30%) and during terminal stance prior to toe-off (45-60%).Knee power variability was greater in the CTRL group throughout most of the stance phase (3-60%).

Discussion
This study aimed to determine gait cycle differences in variability in patients with knee OA before and after undergoing a TKA compared to healthy, similarly aged adults.Whereas previous studies were limited to a simple scalar analysis of variability, which provided an estimate of global variability, this study implemented equality of variance comparison at each interval of the gait cycle 13,14 , which provided the location where the gait cycle differences in variability occurred.
Evaluating variability can assess system stability.For example, high variability of physiological outcomes, like heart rate variability, is favourable as it reflects greater adaptability and a wider ability to respond.In other situations, high variability is unfavourable as it represents the inability of the physiological control system to regulate a given parameter 18,19 .It has been suggested that during gait, greater kinematic and kinetic variability is favourable as it reflects adaptability 18 .To the best of our knowledge, there is no accepted variability threshold for TKA.In this study, patients walked at a self-selected pace on a flat surface with no obstacles.Pre-TKA patients already had significantly less sagittal knee moment and knee power variability than controls.The further reduction in sagittal knee moment and power variability after TKA, particularly during single-limb support, could mean patients are less stable and less capable of adapting to unanticipated situations while walking.
It is estimated that 7-38% of TKA recipients experience a fall within the first 12 months after TKA 20,21 .Reduced movement adaptability can affect a TKA patient's ability to respond to walking disturbances, such as stepping over an obstacle or regaining balance after perturbation, which may lead to a fall 22 .However, this variability reduction may result from movement strategies patients utilize to reduce pain and loading on the affected knee.Studies have shown that individuals with OA on the medial compartment of the knee 8 and after TKA walk with a 'stiff knee gait pattern' characterized by prolonged muscle contractions during the stance phase 23 .Patients could increase the co-contraction around the knee to increase stability but reduce their movement variability 17 .
Passive knee stabilization is achieved through knee ligaments, whereas muscles around the knee achieve active stability, and both systems work together to allow reliable knee joint function 24 .These structures provide proprioceptive feedback to allow for the perception of joint movements and the position of joint segments in space.In the knee, proprioception provides three fundamental functions, stabilization during the static posture, protection against excessive and possible injurious movements via reflex responses, and coordination of complex movements and precise knee joint motions 25 .Proprioceptive feedback is negatively affected in individuals with knee OA, but removing damaged structures during TKA has been reported to improve this proprioceptive feedback 3 .However, this improvement in proprioception and joint stability after TKA is accompanied by a further reduction in variability.This may be due to proprioceptive feedback being primarily supplied by the mechanoreceptors in ligaments and muscle tendons 26 .The TKA implants used in this study required the sacrifice of both the ACL and PCL, which could potentially diminish proprioceptive feedback.These changes need to be better understood with predicting joint function and variability.This study was not designed to determine the source of the decreased movement variability following TKA.However, one possible explanation could be the cruciate sacrificing design of the implants used in this study.The implants in this study (Zimmer Biomet® NexGen® and MicroPort EVOLUTION®) have cruciate sacrificing tibial inserts, meaning the anterior and posterior cruciate ligaments were removed during surgery.These cruciate ligaments play an essential role in the passive stabilization of the knee 24 , so the muscles may have to compensate for this reduced stability by creating more co-contraction, ultimately reducing gait variability 15 .Alternative implant designs preserve the posterior or both cruciate ligaments, improving proprioception more than the cruciate sacrificing TKA 27 .A future study should test this hypothesis by comparing gait variability and muscle activity between various implant designs to determine if the implant design affects gait variability.Although TKA successfully reduces pain and improves strength around the knee, patients still move with atypical movement patterns suggesting an adapted movement pattern to reduced pain while awaiting TKA 28 .Several strategies to reduce variability have been identified, including stiffening the knee joint through co-contraction, walking slower, or paying more attention while walking 21 , which could have been used by the patients in this study.These strategies do not imply conscious cognitive involvement, as it is suspected that patients do not know how they are adapting or why they are doing so 15,29 .The knee OA patients in this study walked with less variability than the controls (Fig. 1), so the further reduction in variability may have been due to these movement strategies they adopted due to the OA, which were further reduced due to either the implant design or the surgery itself.
This study evaluated TKA implants with cruciate sacrificing inserts, so the findings of this study cannot be generalized to all implant types.It also assessed patients after 12 months of surgery.Patients' functions may continue to improve beyond this time 30 , so gait variability may increase over time.Variability analysis may be a potential measure of recovery after TKA, so studies should continue to determine if, post-operatively, patients can match their pre-TKA variability levels or even achieve values closer to healthy controls.Future research is necessary to determine the source for the reduction in variability and whether it is due to the cruciate sacrificing design of TKA implants, an unresolved adaptation developed while awaiting TKA, or other unknown reasons.
Like many biomechanical studies, this study had a relatively small sample size which may increase the risk of type II errors 31 .Some evidence has shown that gait variability associated with knee OA is sex-dependent 8 .To overcome this shortcoming, we included the same number of female and male participants in the implant groups and had an equal number of females and males in the control group.The CTRL group had significantly lower BMI than the TKA group at both pre-and post-operative visits.Although this likely did not influence the KOOS findings 32 , it may partially explain differences in variability as a recent study found that stride length CV increased significantly as body fat percentage increased 33 .
In conclusion, this study identified that patients with knee OA had reduced knee moment variability throughout the stance phase compared to healthy participants of similar age.Knee moment and power variability further decreased following TKA and could not provide movement variability like the controls.Participants were outfitted with 45 passive-reflective markers placed on anatomical locations using the University of Ottawa Motion Analysis Model (UOMAM) 38 .Participants completed a static trial and five trials of level walking at their preferred, self-selected walking speed.The starting spot for each participant was selected so their first step onto the force platform was always done with the affected limb.The TKA groups completed their first visit within one month of surgery, and 12 months (± 1 month) after surgery, the CTRL group completed one visit.
Motion capture data were processed using Vicon Nexus 2.9.2 software (Oxford Metrics, Oxford, UK).Trajectories were filtered using a Woltring filter with a mean, standard error of 15 mm and force platform data using a 4th-order (zero lag) Butterworth filter with a cut-off frequency of 10 Hz.Gait event detection was done with the assistance of the ground reaction forces.Trials were modelled with the UOMAM 38 , and relevant data were extracted with a custom-written Matlab script (2019b, MathWorks, Natick, USA).Walking speed was extracted and normalized to leg length.Knee variables of interest included sagittal and frontal angles and moments and knee joint power.Knee angles were normalized to 100% gait cycle, whereas knee moments and powers were normalized to 62% stance phase 11 .Data were extracted from the affected limb in the TKA groups and the dominant limb in the CTRL group 19 , defined as the participants' preferred leg to kick a ball 39 .All five trials were included in the final analyses and were not averaged together.

Statistical analyses
Scalar variance comparison was completed using the coefficient of variation (CV), which was calculated and compared to the equality of variance results (Eq. 1) 11 .
N is the number of intervals.X is the amplitude of the variable of interest at the ith interval.σ 2 i is the standard deviation of X at the ith interval.
Statistical analyses for the KOOS, CV, and walking speed variables were processed using the SPSS v.27 software (IBM Corporation, Armonk, USA).A One-Way Analysis of Variance with a Bonferroni post-hoc correction was used for the between-group comparisons, and significance was set to p < 0.05 for all comparisons.Effect size is reported as ω 2 for ANOVA.
Knee joint angle, moment, and power variability were compared between the pre-TKA, post-TKA, and control groups using the equality of variance test.Equality of variance was compared between the groups using the 'gwv1d' function 13 in Matlab. (1)

Figure 1 .
Figure 1.Group means and standard deviations (SD) for sagittal knee angles (degrees), moments (Nm/kg), and powers (W/kg) for the pre-operative TKA, post-operative TKA, and control groups.Horizontal bars represent where in the movement cycle differences in variability occur and identify which group had greater variability (p < 0.05).

Figure 2 .
Figure 2. Consolidated Standards of Reporting Trials (CONSORT) flow diagram for enrolled patients.

Table 1 .
Group mean (SD) demographic, walking speed, and Knee injury and Osteoarthritis Outcome Score (KOOS) values.Significant values are in[bold].Bonferroni post hoc comparisons represented by: * significant (p < 0.05) within-group difference between pre-and post-operative TKA visits, and § represents significant (p < 0.05) difference from CTRL.